Star like object that appeared moving slowly due south then increased speed. Did not change direction.

While walking in Dick Kleberg County park at 0547 spotted an object that looked at first like a star that was stationary, then began to move at first slowly then increased speed. It was too far away to judge speed, but I first spotted the object at about 45 degrees looking due west and it dissappeared at about 110 degree, the event lasting about a minute. Object gave appearce of a star, whitish in color, but did not twinkle, no blinking, more like the reflection of light from an object sufficiently high in the atmosphere reflect sunlight despite that it was still very dark in the park. I have walked in the park for the last 18 months from 0530 to 0630 and have essentially identified all the air traffic that flies overhead from the airports in the vicinity, and this object was a new object and did not appear to be an aircraft.